Appearing on "Fox News Sunday," the Republican politician said the ongoing military efforts in Iraq have devolved into three key battles for future stability in the country.
"The fight against al-Qaida in Anbar has turned our way dramatically because the Anbar province is now liberated from al-Qaida because Sunni Arab Iraqis aligned with us to fight al-Qaida, and that's been a great success story, the surge," Graham said.
Graham also identified the fight against Kurdish separatists in northern Iraq and the battle against Iranian-backed Shiite militants as the other key struggles in Iraq.
Sen. Jack Reed, D-R.I., meanwhile, used his time on the show to call for the withdrawal of U.S. troops from Iraq.
"An indefinite, open-ended commitment will not prompt the Iraqi political leaders to take important steps politically which they must take," he said.
"And this course of action is grounding -- grinding down our military forces, our land forces. Readiness is down. Our troops are seeing a treadmill in and out of Iraq. We have to change that."